{"id": "c137", "title": "C137 — The nearest admitted P6 correction is unique", "filename": "490d_C137_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 137, "sha256": "e9b76d59bcb514daccc9ab38ab98f9d23c731db54aca3095967d740298d3c79a", "bytes": 2256, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C136_C155_529_Square_Batch_20260923/C137/490d_C137_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/e9b76d59bcb514daccc9ab38ab98f9d23c731db54aca3095967d740298d3c79a.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C137 — The nearest admitted P6 correction is unique\n\n23 September 2026 · Bounded step 2 of 20 (C136–C155).\n\nAmong the six retained alternate MT Flood pairs, M=2650 gives P6's unique nearest approach to a 2K-sided square. Once its 17K diagonal is held, U is forced to 6343.\n\nThe formal exact choice U=6342, M=2651 has nei", "content": "# C137 — The nearest admitted P6 correction is unique\n\n23 September 2026 · Bounded step 2 of 20 (C136–C155).\n\n**Among the six retained alternate MT Flood pairs, M=2650 gives P6's unique nearest approach to a 2K-sided square.** Once its 17K diagonal is held, U is forced to 6343.\n\nThe formal exact choice U=6342, M=2651 has neither source-field endpoint. The nearest admitted choice is U+1=6343 and M−1=2650. These opposite base changes preserve U+M=8993 and increase both side widths from 1058 to 1059. This compares different candidate endpoints; no historical event is moved.\n\nAll six alternatives satisfy U+M=17K, so uniqueness concerns the **smallest positive side residual**, not uniqueness of every sourced square:\n\n| M | Forced U | Side | Side minus 2K |\n|---|---|---|---|\n| 2645 | 6348 | 1064 | 6 |\n| 2646 | 6347 | 1063 | 5 |\n| 2647 | 6346 | 1062 | 4 |\n| 2648 | 6345 | 1061 | 3 |\n| 2649 | 6344 | 1060 | 2 |\n| 2650 | 6343 | 1059 | 1 |\n\nThis boundary optimization is conditional on the retained 17K diagonal and source fields. It is not independent evidence that 17K itself was uniquely selected by chronology. The next step audits all six alternatives with their actual Gear and start/close tags.\n\n## Source and scope control\n\nAll numerical bases in this packet stand for paired coordinates: BC base B is (B+1)t/Bn BC; reflected AD base A is AD At/(A+1)n. Thus a cross-Mirror same-season span is B+A, after the civil no-year-zero subtraction. AD stations are reflected source events, not historical AD occurrences. K=529 throughout.\n\nRegular Gears remain restricted to Noah/Shem/Flood. Creation and Conquest are fixed source-field selections. C133–C135 corrections remain controlling. The C127 graph and canonical controls are frozen; source-field admission is distinguished from an existing graph node and from a generated comparison coordinate. No wider N01/N03 expansion or missing N03 Shem join is repaired. Original Reports 01–10 remain previously verified references; interrupted original Reports 11–25 remain unestablished. Check counts are computational assertions, not independent historical witnesses.\n\nEvidence: `CERTIFICATE.json`; **22 passing assertions** in `RESULTS.json`. The assertion list identifies the actual tests.\n"}